If you're sure you're going to do the reissue within 24 hours, then ask the RTW desk (or DUB) to prepare a "Price Quote" or "Phase 4" record for ticket issuance. It is valid 24 hours. This will cut down the time as although the ticketing agent will most likely still call the fares desk as he/she doesn't see many RTWs, the desk will just tell him/her that everything is OK and to just issue the tickets as stored in the system. Without the stored PQ or Phase IV record, the desk would have to recalculate the ticket on the spot, which takes loads of time, while you're there waiting.